Registration Deadline: January 24, 2027

Instructor: Professor Ian Hambleton, McMaster University

Course Dates: January 7 - April 5, 2027
Mid-Semester Break: February 15-19, 2027
Lecture Time: Mondays & Thursdays | 10:30 AM - 12:00 PM (ET)
Office Hours: Mondays & Thursdays | 1:00 PM - 2:30 PM (ET)

Registration Fee:

• Students from our Principal Sponsoring & Affiliate Universities: Free
• Other Students: CAD$500

Capacity Limit: 30 students (Auditing is allowed; please indicate so in the registration form)

Format: 

• In-Person: Mondays at HH 312, McMaster University | Thursdays at Room 210, Fields Institute
• Online: via Zoom

Course Description

Selected topics: Morse theory, cobordism, classification of manifolds; introduction to Yang-Mills gauge theory (PDE on smooth 4-manifolds), applications to smooth vs topological structures on 4-manifolds, finite group actions.

Prerequisites: MSc level preparation in Algebra (groups, rings, fields),  Analysis (real and complex, differential forms), and Topology (fundamental groups, covering spaces, homology, manifolds, vector bundles).

Web Resources: Please consult the course webpage on the Fields LMS (learning management system) for all announcements, assignments, and supplementary resrouces.

NOTE: Registration on the Fields LMS is required to access the Zoom link and course materials!

Reading List:

• Bott, Raoul; Tu, Loring W. "Differential forms in algebraic topology". Graduate Texts in Mathematics, 82. Springer-Verlag.
• Warner, Frank W. "Foundations of differentiable manifolds and Lie groups". Graduate Texts in Mathematics, 94. Springer-Verlag.
• Freed, Daniel S.; Uhlenbeck, Karen K. "Instantons and four-manifolds". Mathematical Sciences Research Institute Publications, 1. Springer-Verlag.

Course Assessment (TBA): The course assessment will include evaluation of problem assignments, and a written project report together with an in-class presentation (if time permits).